Explicit representation of finite predictor coefficients and its applications
The Annals of Statistics · 2006 · Volume 34 · Issue 2
DOI: 10.1214/009053606000000209
Abstract
We consider the finite-past predictor coefficients of stationary time series, and establish an explicit representation for them, in terms of the MA and AR coefficients. The proof is based on the alternate applications of projection operators associated with the infinite past and the infinite future. Applying the result to long memory processes, we give the rate of convergence of the finite predictor coefficients and prove an inequality of Baxter-type.
Keywords
60G25, 62M10, 62M20, AR coefficients, Baxter’s inequality, fractional ARIMA processes, long memory, MA coefficients, Predictor
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